Most of us have a rough
idea that computers are
made up of complicated hardware and software. But perhaps few of us
know that the concept of a computer was envisioned long before these
machines became ubiquitous items in our homes, offices and even
pockets.

In 2004 three physicists decided to dabble in a field they knew little about. Within weeks they had developed a new technique that transforms weeks' worth of computer calculations into something that could be done on a single page in an hour. It's used in particle accelerators such as the LHC at CERN.

The natural logarithm is intimately related to the number e and that's how we learn about it at school. When it was first invented, though, people hadn't even heard of the number e and they weren't thinking about exponentiation either. How is that possible?